Not many outside Libya's capital went by plane (4)
I believe the answer is:
flew
'went by plane' is the definition.
(I've seen this in another clue)
'not many outside libya's capital' is the wordplay.
'not many' becomes 'few' (similar in meaning).
'outside' indicates putting letters inside (some letters go outside others).
'capital' says to take the initial letters.
The first letter of 'libyas' is 'l'.
'few' going around 'l' is 'FLEW'.
(Other definitions for flew that I've seen before include "Dashed" , "Rushed (by air?)" , "bolted" , "Travelled by air" , "lip" .)